A dimensionless quantity

may have a unit

A dimensionless quantity is a quantity that does not have any physical units, meaning it is a pure number. This type of quantity is typically the result of a ratio or product of physical quantities where all units cancel each other out.

Detailed Explanation:
In physics and mathematics, quantities are usually measured in terms of physical units like meters, kilograms, or seconds. However, a dimensionless quantity is different because it has no units. It is essentially a number that arises from the relationship between physical quantities whose units cancel each other out during calculation.

For example, in the case of Supplementary Physical Quantities, such as the Reynolds number in fluid dynamics or friction coefficient, the dimensions of all the involved physical quantities (like mass, length, and time) cancel out, leaving behind a pure number. These dimensionless quantities often provide important insights into physical phenomena and can be used in various calculations where unit independence is necessary.